I once splurged and bout a full set of Blick watercolor markers for 250. They're fairly cheaper than copic and I'm still very happy with them today.
I was also thinking, if you want to spend even less, buy a full set of prisma (or Blick) colored pencils and a watercolor colorless blender. Looks just as good as marker and you can play around with colors more.
If you want to go the greyscale route, you can use both options I stated above, but only purchase the greyscale packs.
You can also buy a few paintbrushes and India ink. You can do a lot with just these few things and it only costs around $10. Looks very professional imo and very fun to use!
Can do this sort of thing with them (Not mine)

Very crisp and clean, works well with micron.